一般光學透鏡的成像會受到繞射極限的影響，使得解析度無法小於二分之一的波長。這在電子微影製程或是微生物觀察等應用方面，都會造成限制。因此做出一個突破繞射極限的光學透鏡，便成為人類長久以來的夢想。本論文所探討的雙曲透鏡，便是一種可以突破此限制的光學結構。 電磁波雙曲透鏡是利用金屬與介電質，週期層狀排列的圓柱狀結構。它讓物體的成像能突破繞射極限並具有放大效果。利用等效介質的觀念能幫助我們預測模擬結果的主要特徵。本論文除了介紹雙曲透鏡的基本理論、模擬方法以及電磁波與聲波的類似性外，還針對電磁波雙曲透鏡的特性做各種探討。此外，本論文還利用負的動力學質量密度的概念，成功地設計出一個聲波版本的雙曲透鏡，並透過數值模擬驗證其功能。期望本文的研究結果能對超音波掃描或水底聲納的解析提升做出一點貢獻。Conventional optical lens suffers from a physical restriction called diffraction limit. It not only makes the resolution of a lens unable to be lowered than half a wavelength, but also leads to other constraints in photolithography process and micro-organism observation. Therefore, making an optical lens which can beat the diffraction limit is one of mankind's dreams. Recently, hyperlens was proposed as a solution to overcome the diffraction limit. In this thesis, we study the optical characteristics of hyperlens thoroughly and explore its resolution ability. EM hyperlens is a cylindrical structure consisting of periodically arranged metallic and dielectric material layers. It makes the image of a subwavelength object magnified and breaks the diffraction limit. The main feature of simulation result can be predicted by using the concept of effective medium. In this paper, we introduce the basic theories, simulation methods, the analogies between the electromagnetic and acoustic wave systems, and discuss various properties of EM hyperlens as well. Besides, we also propose an acoustic hyperlens based on the concept of negative dynamic density. Its hyperlens properties are confirmed successfully via numerical simulations. We hope the research results in this thesis can make contributions to improving the resolution of ultrasonics or sonar systems in the future.
